Distributed Utility Maximization for Network Coding Based Multicasting: A Critical Cut Approach

A central issue in practically deploying network coding in a shared network is the adaptive and efficient allocation of network resources. This issue can be formulated as an optimization problem of maximizing the net-utility — the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning. We develop a primal-subgradient type distributed algorithm to solve this utility maximization problem. The effectiveness of the algorithm hinges upon two key properties we discovered: (1) the set of subgradients of the multicast capacity is the convex hull of the indicator vectors for the critical cuts, and (2) the complexity of finding such critical cuts can be reduced by exploiting the algebraic properties of linear network coding. The extension to multiple multicast sessions is also carried out. The effectiveness of the proposed algorithm is confirmed by simulations on an Internet Service Provider’s topology.